Bernoulli Statistics Research Articles

Sampling volumes in powder diffraction experiments

We present a simple analytical formalism based on the Lorentz-Scherrer equation and Bernoulli statistics for estimating the fraction of crystallites (and the associated uncertainty parameters) contributing to all finite Bragg peaks of a typical powder pattern obtained from a static polycrystalline sample. We test and validate this formalism using numerical simulations, and show that they can be applied to experiments using monochromatic or polychromatic (pink-beam) radiation. Our results show that enhancing the sampling efficiency of a given powder diffraction experiment for such samples requires optimizing the sum of the multiplicities of reflections included in the pattern along with the wavelength used in acquiring the pattern. Utilizing these equations in planning powder diffraction experiments for sampling efficiency is also discussed.

CODEX: Stochastic Encoding Method to Relax Resistive Crossbar Accelerator Design Requirements

A stochastic input encoding scheme (CODEX) is presented that aims to relax the analog-to-digital converter (ADC) design requirements in memristor crossbar systems. CODEX reduces the ADC input range by encoding the input bits using Bernoulli statistics so that the bit-line current distribution becomes a narrow Gaussian. By reducing ADC input range, CODEX can be used to reduce ADC power and area or increase ADC resolution to reduce the number of epochs required for in-situ training. Besides input data encoding, CODEX includes probability thresholding for sparse input data as well as a random re-sampling method for dealing with ADC overflow. CODEX is evaluated on CIFAR-10 dataset image classification and reconstruction, sentiment classification, and audio classification. The results show an averaged 68.5% reduction in ADC power, 35.5% reduction in ADC area, and 25.8% reduction in training epochs required for in-situ training when applied to the state-of-the-art ISAAC and PUMA accelerators.

Strategy for rational control of stereosequence in free radical polymerization of acrylates

ABSTRACTRadical polymerization of cyclic analogs of acrylates, (S)‐ and (R)‐2‐isopropyl‐5‐methylene‐1,3‐dioxolan‐4‐ones (1S and 1R), successfully afforded a functional polymer having the tacticity continuously controlled from 29% to ∼100% of meso triad (mm) over a wide range of temperature only by changing the molar ratio of 1S/1R in feed. Plot of the number fractions of the triad versus diad of poly(1) was in good agreement with the Bernoulli statistics. In the polymerization in chiral solvents having analogs structure of the monomers, the tacticity and specific rotation of the resulting polymer were specifically varied depending on the structure and concentration of the solvents. Model propagation reaction at dimeric radical calculated with density functional theory reproduced a methodical induction of the chirality to the main chain from the branched chiral monomeric unit, which supports the experimental expectations. It is remarkable that the ceiling temperature of 1 is tremendously high, for example, 193 °C in [1 (ee = 72.6%)] = 0.05 mol/L, and the isospecific polymerization is maintained even at such a high temperature, which enabled the control of polymer tacticity over a wide range of temperature. The mechanism of the stereosequence in radical polymerization was discussed experimentally and theoretically. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018, 56, 184–193

Robust Estimation of Sparse Narrowband Spectra from Neuronal Spiking Data.

Characterizing the spectral properties of neuronal responses is an important problem in computational neuroscience, as it provides insight into the spectral organization of the underlying functional neural processes. Although spectral analysis techniques are widely used in the analysis of noninvasive neural recordings such as EEG, their application to spiking data is limited due to the binary and nonlinear nature of neuronal spiking. In this paper, we address the problem of estimating the power spectral density of the neural covariate driving the spiking statistics of a neuronal population from binary observations. We consider a neuronal ensemble spiking according to Bernoulli statistics, for which the conditional intensity function is given by the logistic map of a harmonic second-order stationary process with sparse narrowband spectra. By employing sparsity-promoting priors, we compute the maximum a posteriori estimate of the power spectral density of the process from the binary spiking observations. Furthermore, we construct confidence intervals for these estimates by an efficient posterior sampling procedure. We provide simulation studies which reveal that our method outperforms the existing methods for extracting the frequency content of spiking data. Application of our method to clinically recorded spiking data from a patient under general anesthesia reveals a striking resemblance between our estimated power spectral density and that of the local field potential signal. This result corroborates existing findings regarding the salient role of the local field potential as a major neural covariate of rhythmic cortical spiking activity under anesthesia. Our technique allows us to analyze the harmonic structure of spiking activity in a robust fashion, independently of the local field potentials, and without any prior assumption of the spectral spread and content of the underlying neural processes. Other than its usage in the spectral analysis of neuronal spiking data, our technique can be applied to a wide variety of binary data, such as heart beat data, in order to obtain a robust spectral representation.

Sequence distribution of PMMA/iBuA copolymer by incremental calculation of 13C NMR spectra

ABSTRACTAn incremental method for characterizing triad and pentad distribution by 13C NMR spectroscopy was applied to the poly(methyl methacrylate-co-isobutyl acrylate) copolymer. Calculation of the intensity of individual lines was performed applying Bernoulli statistics, while the chemical shifts for each sequence were calculated by an incremental method. Based on these data, the carbonyl signal was simulated yielding good agreement at the triad and pentad level.

Radical Polymerization of Pendant (Meth)acrylates on a Rigid Helical Polyisocyanate Backbone Producing Poly(meth)acrylates with “Ideally” Atactic Main Chain Configuration

This study includes a topic that poly(methyl methacrylate) (PMMA) with an “ideally” atactic main chain configuration, approximately triad tacticities of mm/mr/rr = 1/2/1, has been produced in solution by the “one-dimensionally regulated” radical polymerization using rigid helical polyisocyanate as a macromolecular template. Three types of isocyanate monomers with pendant (meth)acryloxy groups, such as 2-(methacryloxy)ethyl isocyanate (MOI), 2-[2-(methacryloxy)ethoxy]ethyl isocyanate (MOI-EO), and 2-(acryloxy)ethyl isocyanate (AOI), were polymerized using a titanium alkoxide complex to produce the corresponding polyisocyanates, MOI-n, MOI-EO-n, and AOI-n, respectively, in which n represents the number-averaged degree of polymerization. From the SAXS measurements of MOI-26 in hexafluoro-2-propanol and MOI-EO-38 in tetrahydrofuran at 25 °C, the polyisocyanates were found to be considered as rigid rod molecules. The radical polymerization of the pendant (meth)acryloxy groups was performed, and the polyisocyanate template was removed by alkali hydrolysis followed by methyl esterification, eventually producing the poly[methyl (meth)acrylate]s. The diad, triad, and pentad tacicities of the products were determined by the 1H and 13C NMR spectra, and these probabilities followed those calculated based on the Bernoulli statistics. The influences of the polymerization conditions, such as polymerization temperature and monomer concentration, on the tacticity of the final polymers were clarified. The effect of the flexible spacer between the polymerizable group and polyisocynate template was also evaluated. The radical polymerizations in which the polymerizable groups are molecularly regulated on a rod-like helical polyisocyanate backbone produced vinyl polymers with inimitable tacticities even in the solution state.

A logistic non-negative matrix factorization approach to binary data sets

An analysis of binary data sets employing Bernoulli statistics and a partially non-negative factorization of the related matrix of log-odds is presented. The model places several constraints onto the factorization process rendering the estimated basis system strictly non-negative or even binary. Thereby the proposed model places itself in between a logistic PCA and a binary NMF approach. We show with proper toy data sets that different variants of the proposed model yield reasonable results and indeed are able to estimate with good precision the underlying basis system which forms a new and often more compact representation of the observations. An application of the method to the USPS data set reveals the performance of the various variants of the model and shows good reconstruction quality even with a low rank binary basis set.

Bioinformatic analysis of protein families for identification of variable amino acid residues responsible for functional diversity

Proteins within a single family usually share a common function but differ in more specific features and can be divided into subfamilies with different properties. Availability of genomic, structural, and functional information implemented into numerous databases provides new opportunities for bioinformatic analysis of homologous proteins. In this work, new method of bioinformatic analysis has been developed to identify subfamily-specific positions (SSPs) – conserved only within protein subfamilies, but different between subfamilies – that seem to play important role in functional diversity. A novel scoring function is suggested to consider structural information as well as physicochemical and residue conservation in protein subfamilies. Random shuffling is performed to rank results by significance, and Bernoulli statistics is applied to calculate p-values. Algorithm does not require predefined subfamily classification and can propose it automatically by graph-based clustering. This method can be used as a tool to explore SSPs with different structural localization in order to understand their implication to structure–function relationship and protein function. Web interface to the program is available at http://biokinet.belozersky.msu.ru/zebra.

Kinetic Monte Carlo Studies on the Importance of the Reaction Scheme in Segmental Exchange of Copolymer Chains

Kinetic Monte Carlo studies (confirmed by integration of the corresponding differential equations) are used to demonstrate the fundamental differences between the two most often accepted schemes of segmental exchange. Modeling of reshuffling systems, originally composed of homopolymers of various , various mass distributions, and different compositions, is carried out until the equilibrium copolymers are obtained. It is shown that one of the schemes leads always to a random microstructure (Bernoulli statistics) whereas modeling of the other one indicates possibility of formation of all achievable distributions of comonomer units (from multiblock to nearly alternate). The concepts of the degrees of randomness and reshuffling are discussed and new definitions are proposed.

Facile synthesis of stereoregular carbon fiber precursor polymers by template assisted solid phase polymerization

Predominantly isotactic stereoregular polyacrylonitrile copolymers (PAC) were prepared by solid phase polymerization techniques using hexagonal crystalline metal salts as template compounds. Stereoregular distributions of the prepared polymer were studied using high resolution 13C nuclear magnetic resonance spectroscopy (13C NMR) spectra. The extent of isotacticity was directly determined from the peak intensity of the methine carbon (CH). The triad tacticity from the intensities of methine carbon peaks were examined by statistical methods. It was found that the PAC was predominantly isotactic in stereoregularity, and its sequence distribution obeys Bernoulli statistics. The optimum polymerization conditions ensuring isotactic content over 50% were disclosed experimentally. The chemical composition of PAC was confirmed with 1H NMR data. The obtained polyacrylonitrile copolymers were also characterized for molecular parameters such as viscosity average molecular weight (Mv), number average molecular weight (Mn), weight average molecular weight (Mw) and polydispersity index.

The effect of synthesis conditions on the microheterogeneity of the butadiene-isoprene copolymer

The dependence of the microheterogeneity of butadiene-isoprene copolymers synthesized in the presence of a titanium-based catalytic system on the hydrodynamic regime used at the initial moment of formation of the reaction mixture of copolymerization is studied. When copolymers are synthesized with the direct addition of the catalyst to the solution of the comonomers, copolymers featuring a statistical distribution of units are formed, regardless of the composition of the initial comonomer mixture. In this case, the growth of copolymer chains obeys the Bernoulli statistics. Depending of the composition of the initial comonomer mixture, hydrodynamic factors promote different extents of deviation from the statistical growth of copolymer chains.

A closed form solution of Bernoullian two-classes priority queue

We investigate the effect of a two-priority policy when serving slotted traffic arriving with Bernoulli statistics. We are able to give explicit closed-form expressions for the distribution of the lengths of the high- and low-priority queue.

A closed form solution of bernoullian two-classes priority queue

We investigate the effect of a two-priority policy when serving slotted traffic arriving with Bernoulli statistics. We are able to give explicit closed-form expressions for the distribution of the lengths of the high- and low-priority queue.

Molecular architecture of poly[(R,S)-3-hydroxybutyrate-co-6-hydroxyhexanoate] and poly[(R,S)-3-hydroxybutyrate-co-(R,S)-2-hydroxyhexanoate] oligomers investigated by electrospray ionization ion-trap multistage mass spectrometry.

A series of aliphatic copolyesters was obtained from (R,S)-beta-butyrolactone and two isomeric hydroxy acids, 6-hydroxyhexanoic and (R,S)-2-hydroxyhexanoic acids. The reactions were conducted in bulk without catalyst. Electrospray ionization tandem mass spectrometry (ESI-MSn) was used for molecular characterization of these copolyester oligomers. The mass spectra of the copolyesters studied have enabled identification of their molecular structures including chemical nature of the end groups (hydroxyl and carboxylate). The compositions of the oligocopolyesters and their sequence distributions were determined based on measurement of the relative intensities of the individual oligocopolyester peaks in the ESI mass spectra. The mass spectra (MS1) provided information on composition and sequence distribution, and small deviations from Bernoulli statistics were detected. The arrangement of co-monomer structural units along the oligopolyester chains was verified by MS/MS experiments and investigation of the fragmentation pathways.

Monte Carlo simulation of AB-copolymers with saturating bonds

Structural transitions in a single AB-copolymer chain where saturating bonds canbe formed between A-and B-units are studied by means of Monte Carlo computersimulations using the bond fluctuation model. Three transitions are found,coil–globule, coil–hairpin and globule–hairpin, depending on the nature of aparticular AB-sequence: statistical random sequence, diblock sequence and‘random–complementary’ sequence (one-half of such an AB-sequence is randomwith Bernoulli statistics while the other half is complementary to the first one).The properties of random–complementary sequences are closer to those of diblocksequences than to the properties of random sequences. The model (although quiterough) is expected to represent some basic features of real RNA molecules, i.e. theformation of secondary structure of RNA due to hydrogen bonding ofcorresponding bases and stacking interactions of the base pairs in helixes. Weintroduce the notation of RNA-like copolymers and discuss in what sense thesequences studied here can be considered as RNA-like copolymers.

Study on the Stereoregularity of Polyacrylonitrile Produced by Precipitation Polymerization in Supercritical CO2

The triad and pentad tacticities of PAN obtained by precipitation polymerization in supercritical carbon dioxide, using AIBN as initiator, (hereafter, referred as CO2-PAN) were analyzed by 13C NMR and IR method. The pentad tacticities of CO2-PAN from the intensities of cyano peaks were examined by statistical methods. It was found that CO2-PAN was completely random in stereoregularity, and the sequence distributions of it obey Bernoulli statistics. Compared with the aqueous phase suspension polymerization of AN, using AIBN as initiator, (hereafter, referred as S-PAN) and aqueous phase precipitation polymerization of AN, using redox type initiator, (hereafter, referred as R-PAN), it was found isotacticity of CO2-PAN was lower than those of S-PAN and R-PAN, although the three kinds of PAN were all random in stereoregularity. The reason is probably due to the different polar property of solvent used. The relation between IR data and stereoregularity of PAN has also been used to calculate the isotactic triad units of CO2-PAN, the result is accordant with the 13C NMR method used.

Concepts for preparation of novel regioselective modified cellulose derivatives sulfated, aminated, carboxylated and acetylated for hemocompatible ultrathin coatings on biomaterials

Some regioselective cellulose derivatives were synthesized on the basis of the just started longterm concept by variation of O-SO 3 , N-SO 3 , N-Ac, and N-carboxymethyl groups solely or in combination for the development of athrombogenic and antithrombogenic nanocoatings on cellulose membranes. Similar regioselectively arranged functional groups are known partially in type 1 glycosaminoglycane (dermatan sulfate DS, and chondroitin sulfate CS) and all the groups are present in type 2 GAC (heparin HE and heparansulfat HS). The goal of this concept was to use instead of the backbone structure β 1 ->4, β 1->3 (DS, CS) or β 1->4, α &6>4 (HE, HS or regioselective desulfated HE, the β 1->4 backbone structure of cellulose or chitosan, with the same functional groups as in HE. Furthermore different regioselective sulfated cellulose derivatives, such as cellulose636sulfate, cellulose-2,6-disulfate, and cellulose-2,3-sulfates with varied sulfation degrees have been synthesized and immobilized ionically on cellulose membranes. They were tested concerning their reduction of platelet adhesion from citrated whole blood in a perfusion system as well for AT III affinity. The lowest latelet adhesion and AT III affinity was observed using cellulose-2,3-sulfates and cellulose-3-sulfate derivatives, whereas cellulose-6-O-sulfate derivatives show high AT III affinity and high platelet adhesion. This means that a high 6-O-sulfate content seems to promote anticoagulant properties of the derivatives with high (AT III) affinity, whereas low concentrations of 2-O- and 3-O-sulfate groups show the lowest platelet adhesion. The latter seems to be important for developing athrombogenic coatings for biomaterials. The starting material chitosan with molecular weight of 150 KD was used to synthesize additionally some of 2-deoxyaminocellulose derivatives containing N-Ac or N-SO 3 or N-CH 2 -COOH and O-SO 3 group. These derivatives are structurally closer to HE and HS and should enable us to work out the influence of each heparin like functional group in cellulose derivative on the athrombogenic and antithrombogenic properties. We synthesized only some of the latter mentioned derivatives with a distribution of the functional groups according to a Bernoulli statistics. Totally sulfated 2-deoxyaminocellulose-3,6-disulfate derivatives will be regioselectively desulfated by reactions known from heparin chemistry.

Production variability in manufacturing systems: Bernoulli reliability case

The problem of production variability in serial manufacturing lines with unreliable machines is addressed. Bernoulli statistics of machine reliability are assumed. Three problems are considered: the problem of production variance, the problem of constant demand satisfaction, and the problem of random demand satisfaction generated by another (unreliable) production line. For all three problems, bounds on the respective variability measures are derived. These bounds show that long lines smooth out the production and reduce the variability. More precisely, these bounds state that the production variability of a line with many machines is smaller than that of a single machine system with production volume and reliability characteristics similar to those of the longer line. Since all the variability measures for a single machine line can be calculated relatively easily, these bounds provide analytical tools for analysis and design of serial production lines from the point of view of the customer demand satisfaction.

Bottlenecks in assembly systems: Identification and application

Bottlenecks (BNs) in assembly lines with unreliable machines and finite buffers are analyzed. Bernoulli statistics of machines breakdowns are assumed. A method for BN identification is developed. This method requires expressions of the system's production rate and the probabilities of machines blockages and starvations as functions of the machines and buffers parameters. Accordingly, the paper develops a method for evaluating these functions and then applies it to BN analysis. All steps of the development are illustrated by a case study carried out at an automotive component plant.

Production variability in manufacturing systems: Performance bounds and monotonicity properties

Production variability in serial manufacturing lines with unreliable machines and finite buffers is addressed. Bernoulli statistics of machines breakdowns are assumed. Two problems are considered: the problem of production variance and the problem of constant demand satisfaction. For both problems, bounds on the respective variability measures are derived. Counter-intuitively, these bounds show that the production variability of a line with many machines is smaller than that of a single machine having the production volume and reliability characteristics similar to those of the longer line. Since all the variability measures for a single machine can be calculated relatively easily, these bounds provide analytical tools for analysis and design of serial production lines from the point of view of the customer demand satisfaction. In addition, monotonicity properties of the variability measures with respect to machines and buffers parameters are investigated and, again counter-intuitively, it is shown that improving machines and/or increasing buffers may not lead improved production variability. A sufficient condition under which this improvement does, in fact, take place is derived.